In this paper we prove that Basic Logic (BL) is complete w.r.t. the continuous t-norms on [0,1], solving the open problem posed by Ha Âjek in [4]. In fact, Ha Âjek proved that such completeness theorem can be obtained provided two new axioms, B1 and B2, were added to the original axioms of BL. The main result of the paper is to show that B1 and B2 axioms are indeed redundant. We also obtain an improvement of the decomposition theorem for saturated BL-chains as ordinal sums whose components are either MV, product or Go Èdel chains, in an analogous way as for continuous t-norms. Finally we provide equational characterizations of the variety of BL-algebras generated by the three basic BL subvarieties, as well as of the varieties generated by each pair of them, together with completeness results of the calculi corresponding to all these subvarieties.Key words many-valued logic (basic, èukasiewicz, product and Go Èdel logics), equational classes, fuzzy logic, t-norms and standard completeness IntroductionBasic Logic (BL for short) and the corresponding algebras (BL-algebras) were introduced by Ha Âjek (see [3] and the references given there) as an attempt to axiomatize the many-valued semantics induced by continuous t-norms on the unit real interval [0, 1].As a ®rst step, Ha Âjek showed that a propositional formula is provable in BL if and only if it is a tautology in any linearly ordered BL-algebra (BL-chain for short). However, completeness of BL w.r.t. the BL algebras in [0, 1] induced by continuous t-norms was left as an open problem in [3].In the recent paper [4], Ha Âjek proved that such completeness theorem can be obtained provided two new axioms, B1 and B2, were added to the original axiomatic system of BL. These new axioms are rather unnatural and without a clear logical meaning. Hence it is natural to ask, as Ha Âjek did, whether they are necessary or can be derived from the original axioms. The aim of this paper is to solve this problem, showing that the new axioms are indeed redundant, i.e., that the original axiomatic of BL is complete w.r.t. the continuous t-norms on [0, 1].After a summary in Sect. 2 of main results of [4], Sect. 3 deals with the structure of BL-chains. Axiom B1 was introduced to prevent the existence of some``pathological triples'' in saturated and irreducible BL-chains. We show (Theorem 3.1) that these pathological triples cannot exist in any BL-chain, without using axiom B1. The role of Axiom B2 was to guarantee that a saturated and irreducible BL-chain with zero divisors is an MV-algebra. We present two proofs of this fact (Lemma 3.3 and Remark 2), neither of them depending on B2. In fact, in Theorem 3.4 we show that any saturated and irreducible BL-chain is either a MV chain or a product chain. In this way we obtain an improvement of the decomposition theorem for saturated Theorem 4]: any saturated BL-chain is an ordinal sum whose components are either MV, product or Go Èdel chains. The analogy between this representation and the well-known decomposition theorem for continuous t-no...

This work aimed to evaluate the potential role of the 5-HT(7) receptor in nociception secondary to a sensitizing stimulus in mice. For this purpose, the effects of relevant ligands (5-HT(7) receptor agonists: AS-19, MSD-5a, E-55888; 5-HT(7) receptor antagonists: SB-258719, SB-269970; 5-HT(1A) receptor agonist: F-13640; 5-HT(1A) receptor antagonist: WAY-100635) were assessed on capsaicin-induced mechanical hypersensitivity, a pain behavior involving hypersensitivity of dorsal horn neurons (central sensitization). For the 5-HT(7) receptor agonists used, binding profile and intrinsic efficacy to stimulate cAMP formation in HEK-293F cells expressing the human 5-HT(7) receptor were also evaluated. AS-19 and E-55888 were selective for 5-HT(7) receptors. E-55888 was a full agonist whereas AS-19 and MSD-5a behaved as partial agonists, with maximal effects corresponding to 77% and 61%, respectively, of the cAMP response evoked by the full agonist 5-HT. Our in vivo results revealed that systemic administration of 5-HT(7) receptor agonists exerted a clear-cut dose-dependent antinociceptive effect that was prevented by 5-HT(7) receptor antagonists, but not by the 5-HT(1A) receptor antagonist. The order of efficacy (E-55888>AS-19>MSD-5a) matched their in vitro efficacy as 5-HT(7) receptor agonists. Contrary to agonists, a dose-dependent promotion of mechanical hypersensitivity was observed after administration of 5-HT(7) receptor antagonists, substantiating the involvement of the 5-HT(7) receptor in the control of capsaicin-induced mechanical hypersensitivity. These findings suggest that serotonin exerts an inhibitory role in the control of nociception through activation of 5-HT(7) receptors, and point to a new potential therapeutic use of 5-HT(7) receptor agonists in the field of analgesia.

A large number of therapeutic roles have been proposed for sigma(1) receptors but the involvement of sigma(1) receptor in non-acute pain had not been well explored up to now. sigma(1) receptor knock-out mice became available offering us the possibility to study the role of sigma(1) receptor in nociception, particularly in models where central sensitization processes play a significant role. Given the attractive therapeutic potential, we have developed a chemical program aimed at the discovery of novel and selective sigma(1) ligands. Herein we discuss the rational basis of this approach and report preliminary pharmacological results of several chemical series and aspects of their structure-activity relationship on sigma(1) receptor. Functional data in pain models are presented mainly on one series that provide evidence to consider selective sigma(1) receptor antagonists an innovative and alternative approach for treating neuropathic pain.

Based on a medicinal chemistry guided hypothetical pharmacophore model, novel series of indolyl sulfonamides have been designed and prepared as selective and high-affinity serotonin 5-HT(6) receptor ligands. Furthermore, based on a screening approach of a discovery library, a series of benzoxazinepiperidinyl sulfonamides were identified as selective 5-HT(6) ligands. Many of the compounds described in this paper possess excellent affinities, displaying pK(i) values greater than 8 (some even >9) and high selectivities against a wide range (>50) of other CNS relevant receptors. First, structure-affinity relationships of these ligands are discussed. In terms of functionality, high-affinity antagonists, as well as agonists and even partial agonists, were prepared. Compounds 19c and 19g represent the highest-affinity 5-HT(6) agonists ever reported in the literature. These valuable tool compounds should allow for the detailed study of the role of the 5-HT(6) receptor in relevant animal models of disorders such as cognition deficits, depression, anxiety, or obesity.

Let K be a variety of (commutative, integral) residuated lattices. The substructural logic usually associated with K is an algebraizable logic that has K as its equivalent algebraic semantics, and is a logic that preserves truth, i.e., 1 is the only truth value preserved by the inferences of the logic. In this paper we introduce another logic associated with K, namely the logic that preserves degrees of truth, in the sense that it preserves lower bounds of truth values in inferences. We study this second logic mainly from the point of view of abstract algebraic logic. We determine its algebraic models and we classify it in the Leibniz and the Frege hierarchies: we show that it is always fully selfextensional, that for most varieties K it is non-protoalgebraic, and that it is algebraizable if and only K is a variety of generalized Heyting algebras, in which case it coincides with the logic that preserves truth. We also characterize the new logic in three ways: by a Hilbert style axiomatic system, by a Gentzen style sequent calculus, and by a set of conditions on its closure operator. Concerning the relation between the two logics, we prove that the truth preserving logic is the extension of the one that preserves degrees of truth with either the rule of Modus Ponens or the rule of Adjunction for the fusion connective.